For this question I'm going to assume that we're talking about food grown outdoors without making use of any greenhouse. Once we allow use of a greenhouse, fresh produce can be grown just about anywhere -- even at the South Pole.
Sweden spans a great deal of latitude, from 55º in the South to 68º in the North. Between those latitudes there is a great deal of agricultural variation, so for the sake of this question I'll assume that 55ºN counts as Nordic country. That still allows a great area of land for domestic production of food, and is indeed where Sweden's centre of agriculture is found.
The climate at this latitude is usually temperate, though in some places will be boreal (sub-arctic). Sweden is temperate in the South and boreal in the North. There is good potential for vegetation and agriculture in a temperate climate, but the sub-arctic climate is probably too hostile to support a healthy plant-based diet entirely on food grown outdoors.
The South of Sweden would be classified as a humid continental climate (
Dfb in the Köppen climate classification system). This is a climate where forests thrive! And where there aren't forests, it's perfectly possible to grow common cereal grains (eg. wheat, flax, rapeseed, barley, oats, or maize) and vegetables like sugar beet. Sweden even has a long history of soy cultivation. It seems that some potatoes are grown in Sweden, but neighbouring Norway seems better known for potatoes.
So far I've described a variety of sources of macronutrients (carbohydrates, fats, and protein). Even some micronutrients that are more easily found in foods from warmer climates (like Vitamin E in avocado) can be reasonably obtained from rapeseed (aka canola).
So in conclusion, yes it seems quite feasible that a person living in a Nordic country such as Sweden or Norway could assemble a healthy and balanced plant-based diet based entirely on foods that are (or could be) grown domestically.